Sydney Olympics 2000

Here is the promised conversion of Scarthin Lattice Labyrinth (40,20) into Olympic Lattice Labyrinth (40,20). Ill explain why the Family names later. Each of the supertiles of the Scarthin Labyrinth have been divided into two by adding a couple of lattice links to separate the central four squares into two terminal twos. The new supertile areas are now of 500 squares each , there being four in four different orientations to make up the 2000 square repeat unit (fundamental domain you might say, maybe) of the tessellation. We now need more than two colours to distinguish the supertiles; three will do and this does disguise the close relation between the two familes, but I’ve been more considerate and have used four for the four different orientations, so you can perhaps see what I’ve done more clearly. Halving the supertiles has allowed me to add some more of them without extending the reach of their flailing arms; the effect is pretty stunningly pretty. Sophie and the 2000’ers can claim this one too if you like.

Olympic(40,20)Notice how each Olympic supertile (light blue, for instance), being one half of an erstwhile Scarthin supertile,  is wound up at one remove inside the other half (dark blue) of an adjacent Scarthin supertile, the two being oriented at 180 degrees to each other. This elegant property is a consequence of the diagonal symmetry of the erstwhile original. To help make sense of it, here is just one supertile, showing the 500 individual squares of which it is made up.

Olympic (40,20) SupertileThis is one of the more spectacular Lattice Labyrinths I’ve brought into the light, even if the choice of colours is not the most artistically educated. I need help from Dulux.

P.S. Links to the revelatory workbook: From the publisher, or via you-know-who , better,  from a good independent bookshop or just Google.


About davescarthin

After a brief academic and local government career, long an independent bookseller/publisher at Scarthin Books, Cromford, Derbyshire, UK. An antiquarian bookseller in two senses, now also has time to be an annuated independent post-doc, developing the long dormant topic of lattice labyrinth tessellations - both a mathematical recreation and a source of compelling practical tiling/paving and textile designs. Presenting a paper and experiencing so many others at Bridges Seoul 2014 Mathart conference was a great treat, as was the MathsJam Annual Conference in November 2016. I'm building up to a more academic journal paper and trying hard to find practical outlets in graphic design and landscape architecture. An 8 ft square tiling design was part of the Wirksworth Festival Art and Architecture Trail 2016. I love giving illustrated talks, tailored to the audience. Get in touch to commission or to collaborate.
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